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<div class="section" id="hashing-feature-transformation-using-totally-random-trees">
<span id="sphx-glr-auto-examples-ensemble-plot-random-forest-embedding-py"></span><h1>Hashing feature transformation using Totally Random Trees<a class="headerlink" href="#hashing-feature-transformation-using-totally-random-trees" title="Permalink to this headline">¶</a></h1>
<p>RandomTreesEmbedding provides a way to map data to a
very high-dimensional, sparse representation, which might
be beneficial for classification.
The mapping is completely unsupervised and very efficient.</p>
<p>This example visualizes the partitions given by several
trees and shows how the transformation can also be used for
non-linear dimensionality reduction or non-linear classification.</p>
<p>Points that are neighboring often share the same leaf of a tree and therefore
share large parts of their hashed representation. This allows to
separate two concentric circles simply based on the principal components
of the transformed data with truncated SVD.</p>
<p>In high-dimensional spaces, linear classifiers often achieve
excellent accuracy. For sparse binary data, BernoulliNB
is particularly well-suited. The bottom row compares the
decision boundary obtained by BernoulliNB in the transformed
space with an ExtraTreesClassifier forests learned on the
original data.</p>
<img alt="../../_images/sphx_glr_plot_random_forest_embedding_001.png" class="align-center" src="../../_images/sphx_glr_plot_random_forest_embedding_001.png" />
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.datasets.make_circles.html#sklearn.datasets.make_circles" title="View documentation for sklearn.datasets.make_circles"><span class="n">make_circles</span></a>
<span class="kn">from</span> <span class="nn">sklearn.ensemble</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.ensemble.RandomTreesEmbedding.html#sklearn.ensemble.RandomTreesEmbedding" title="View documentation for sklearn.ensemble.RandomTreesEmbedding"><span class="n">RandomTreesEmbedding</span></a><span class="p">,</span> <a href="../../modules/generated/sklearn.ensemble.ExtraTreesClassifier.html#sklearn.ensemble.ExtraTreesClassifier" title="View documentation for sklearn.ensemble.ExtraTreesClassifier"><span class="n">ExtraTreesClassifier</span></a>
<span class="kn">from</span> <span class="nn">sklearn.decomposition</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.decomposition.TruncatedSVD.html#sklearn.decomposition.TruncatedSVD" title="View documentation for sklearn.decomposition.TruncatedSVD"><span class="n">TruncatedSVD</span></a>
<span class="kn">from</span> <span class="nn">sklearn.naive_bayes</span> <span class="kn">import</span> <a href="../../modules/generated/sklearn.naive_bayes.BernoulliNB.html#sklearn.naive_bayes.BernoulliNB" title="View documentation for sklearn.naive_bayes.BernoulliNB"><span class="n">BernoulliNB</span></a>
<span class="c1"># make a synthetic dataset</span>
<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.datasets.make_circles.html#sklearn.datasets.make_circles" title="View documentation for sklearn.datasets.make_circles"><span class="n">make_circles</span></a><span class="p">(</span><span class="n">factor</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">noise</span><span class="o">=</span><span class="mf">0.05</span><span class="p">)</span>
<span class="c1"># use RandomTreesEmbedding to transform data</span>
<span class="n">hasher</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.ensemble.RandomTreesEmbedding.html#sklearn.ensemble.RandomTreesEmbedding" title="View documentation for sklearn.ensemble.RandomTreesEmbedding"><span class="n">RandomTreesEmbedding</span></a><span class="p">(</span><span class="n">n_estimators</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">max_depth</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
<span class="n">X_transformed</span> <span class="o">=</span> <span class="n">hasher</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X</span><span class="p">)</span>
<span class="c1"># Visualize result after dimensionality reduction using truncated SVD</span>
<span class="n">svd</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.decomposition.TruncatedSVD.html#sklearn.decomposition.TruncatedSVD" title="View documentation for sklearn.decomposition.TruncatedSVD"><span class="n">TruncatedSVD</span></a><span class="p">(</span><span class="n">n_components</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
<span class="n">X_reduced</span> <span class="o">=</span> <span class="n">svd</span><span class="o">.</span><span class="n">fit_transform</span><span class="p">(</span><span class="n">X_transformed</span><span class="p">)</span>
<span class="c1"># Learn a Naive Bayes classifier on the transformed data</span>
<span class="n">nb</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.naive_bayes.BernoulliNB.html#sklearn.naive_bayes.BernoulliNB" title="View documentation for sklearn.naive_bayes.BernoulliNB"><span class="n">BernoulliNB</span></a><span class="p">()</span>
<span class="n">nb</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_transformed</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="c1"># Learn an ExtraTreesClassifier for comparison</span>
<span class="n">trees</span> <span class="o">=</span> <a href="../../modules/generated/sklearn.ensemble.ExtraTreesClassifier.html#sklearn.ensemble.ExtraTreesClassifier" title="View documentation for sklearn.ensemble.ExtraTreesClassifier"><span class="n">ExtraTreesClassifier</span></a><span class="p">(</span><span class="n">max_depth</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">n_estimators</span><span class="o">=</span><span class="mi">10</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">trees</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="c1"># scatter plot of original and reduced data</span>
<span class="n">fig</span> <span class="o">=</span> <a href="http://matplotlib.org/api/_as_gen/matplotlib.figure.AxesStack.html#matplotlib.figure" title="View documentation for matplotlib.pyplot.figure"><span class="n">plt</span><span class="o">.</span><span class="n">figure</span></a><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">9</span><span class="p">,</span> <span class="mi">8</span><span class="p">))</span>
<span class="n">ax</span> <span class="o">=</span> <a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="View documentation for matplotlib.pyplot.subplot"><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">221</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">X</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="n">y</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">edgecolor</span><span class="o">=</span><span class="s1">'k'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Original Data (2d)"</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(())</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(())</span>
<span class="n">ax</span> <span class="o">=</span> <a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="View documentation for matplotlib.pyplot.subplot"><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">222</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">X_reduced</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X_reduced</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="n">y</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">edgecolor</span><span class="o">=</span><span class="s1">'k'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Truncated SVD reduction (2d) of transformed data (</span><span class="si">%d</span><span class="s2">d)"</span> <span class="o">%</span>
<span class="n">X_transformed</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(())</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(())</span>
<span class="c1"># Plot the decision in original space. For that, we will assign a color</span>
<span class="c1"># to each point in the mesh [x_min, x_max]x[y_min, y_max].</span>
<span class="n">h</span> <span class="o">=</span> <span class="o">.</span><span class="mo">01</span>
<span class="n">x_min</span><span class="p">,</span> <span class="n">x_max</span> <span class="o">=</span> <span class="n">X</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">min</span><span class="p">()</span> <span class="o">-</span> <span class="o">.</span><span class="mi">5</span><span class="p">,</span> <span class="n">X</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o">+</span> <span class="o">.</span><span class="mi">5</span>
<span class="n">y_min</span><span class="p">,</span> <span class="n">y_max</span> <span class="o">=</span> <span class="n">X</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">min</span><span class="p">()</span> <span class="o">-</span> <span class="o">.</span><span class="mi">5</span><span class="p">,</span> <span class="n">X</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o">+</span> <span class="o">.</span><span class="mi">5</span>
<span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.meshgrid.html#numpy.meshgrid" title="View documentation for numpy.meshgrid"><span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span></a><span class="p">(</span><a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.arange.html#numpy.arange" title="View documentation for numpy.arange"><span class="n">np</span><span class="o">.</span><span class="n">arange</span></a><span class="p">(</span><span class="n">x_min</span><span class="p">,</span> <span class="n">x_max</span><span class="p">,</span> <span class="n">h</span><span class="p">),</span> <a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.arange.html#numpy.arange" title="View documentation for numpy.arange"><span class="n">np</span><span class="o">.</span><span class="n">arange</span></a><span class="p">(</span><span class="n">y_min</span><span class="p">,</span> <span class="n">y_max</span><span class="p">,</span> <span class="n">h</span><span class="p">))</span>
<span class="c1"># transform grid using RandomTreesEmbedding</span>
<span class="n">transformed_grid</span> <span class="o">=</span> <span class="n">hasher</span><span class="o">.</span><span class="n">transform</span><span class="p">(</span><a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.c_.html#numpy.c_" title="View documentation for numpy.c_"><span class="n">np</span><span class="o">.</span><span class="n">c_</span></a><span class="p">[</span><span class="n">xx</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">yy</span><span class="o">.</span><span class="n">ravel</span><span class="p">()])</span>
<span class="n">y_grid_pred</span> <span class="o">=</span> <span class="n">nb</span><span class="o">.</span><span class="n">predict_proba</span><span class="p">(</span><span class="n">transformed_grid</span><span class="p">)[:,</span> <span class="mi">1</span><span class="p">]</span>
<span class="n">ax</span> <span class="o">=</span> <a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="View documentation for matplotlib.pyplot.subplot"><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">223</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Naive Bayes on Transformed data"</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">pcolormesh</span><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">,</span> <span class="n">y_grid_pred</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">xx</span><span class="o">.</span><span class="n">shape</span><span class="p">))</span>
<span class="n">ax</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">X</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="n">y</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">edgecolor</span><span class="o">=</span><span class="s1">'k'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">(</span><span class="o">-</span><span class="mf">1.4</span><span class="p">,</span> <span class="mf">1.4</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">(</span><span class="o">-</span><span class="mf">1.4</span><span class="p">,</span> <span class="mf">1.4</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(())</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(())</span>
<span class="c1"># transform grid using ExtraTreesClassifier</span>
<span class="n">y_grid_pred</span> <span class="o">=</span> <span class="n">trees</span><span class="o">.</span><span class="n">predict_proba</span><span class="p">(</span><a href="http://docs.scipy.org/doc/numpy-1.8.1/reference/generated/numpy.c_.html#numpy.c_" title="View documentation for numpy.c_"><span class="n">np</span><span class="o">.</span><span class="n">c_</span></a><span class="p">[</span><span class="n">xx</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">yy</span><span class="o">.</span><span class="n">ravel</span><span class="p">()])[:,</span> <span class="mi">1</span><span class="p">]</span>
<span class="n">ax</span> <span class="o">=</span> <a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.subplot.html#matplotlib.pyplot.subplot" title="View documentation for matplotlib.pyplot.subplot"><span class="n">plt</span><span class="o">.</span><span class="n">subplot</span></a><span class="p">(</span><span class="mi">224</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"ExtraTrees predictions"</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">pcolormesh</span><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">,</span> <span class="n">y_grid_pred</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">xx</span><span class="o">.</span><span class="n">shape</span><span class="p">))</span>
<span class="n">ax</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">X</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">X</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">c</span><span class="o">=</span><span class="n">y</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">edgecolor</span><span class="o">=</span><span class="s1">'k'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">(</span><span class="o">-</span><span class="mf">1.4</span><span class="p">,</span> <span class="mf">1.4</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">(</span><span class="o">-</span><span class="mf">1.4</span><span class="p">,</span> <span class="mf">1.4</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(())</span>
<span class="n">ax</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(())</span>
<a href="http://matplotlib.org/api/tight_layout_api.html#matplotlib.tight_layout" title="View documentation for matplotlib.pyplot.tight_layout"><span class="n">plt</span><span class="o">.</span><span class="n">tight_layout</span></a><span class="p">()</span>
<a href="http://matplotlib.org/api/_as_gen/matplotlib.pyplot.show.html#matplotlib.pyplot.show" title="View documentation for matplotlib.pyplot.show"><span class="n">plt</span><span class="o">.</span><span class="n">show</span></a><span class="p">()</span>
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